**Middle School Number Sense Lesson 68: Adding Squares with One Number being Double the Other**

Last summer we introduced the companion idea (

**AddSquareTrip**) to today's concept. It would probably be a good idea to review that one first, if you haven't done so recently. Today we'll add a little twist to that process--which means we have a whopping 2 or 3 steps to do to solve these. This concept appeared

**9 times**last year, with a median placement at

**question # 67**.

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These questions are usually pretty easy to identify--examples coming shortly. Once you have recognized the pattern, follow these steps:

- Square the smaller number.
- Multiply the result by 5 (or divide by 2 and multiply by 10).

**Example 1:**

**12**

^{2}+ 24^{2}= ___1.

**12**is the smaller number. 12

^{2}=

**144**.

2. Multiply by 5. 144 x 5 =

**720**.

**Example 2:**

**16**

^{2}+ 32^{2}= ___1.

**16**is the smaller number. 16

^{2}=

**256**.

2. Multiply by 5. 256 x 5 =

**1280**.

**Example 3:**

**9**

^{2}+ 18^{2}= ___1.

**9**is the smaller number. 9

^{2}=

**81**.

2. Multiply by 5. 81 x 5 =

**405**.

**Example 4:**

**22**

^{2}+ 11^{2}= ___1.

**11**is the smaller number. 11

^{2}=

**121**.

2. Multiply by 5. 121 x 5 =

**605**.

**Example 5: 32 x 32 + 16 x 16 = ___**

- This is a very clever disguise. Notice that this problem is actually the same as Example # 2, only written as a multiplication (instead of squaring), and with the larger number first.
- Square 16 to get
**256**. - Multiply by 5 to get
**1280**.

**Here's a free worksheet to help you practice AddSquareDoub:**

addsquaredoub.pdf |

**Up Next for Middle School: SquareRootSim**